A river of rectangular cross$-$section in shape has a width of $80$ m and a probable maximum flood of $650$ m$3/$s$.$ The river is unlined, with a Manning roughness coefficient of $0\mathrm{.}015$ and a friction slope of $2\mathrm{.}5\backslash$times $104.$ i$)$ Calculate the critical and normal depths of flow. $(6)$ ii$)$ A barrier is to be constructed across the river mouth in an urban regeneration project, which regulates the depth to $4\mathrm{.}5$ m at the barrier site. By using any appropriate method, estimate the distance along the channel over which the water level will be raised by no more than $2\%$ of the normal depth. In any iterative study you might choose to use, consider no more than $3$ increments.